Question

solve the system of equations below algebraically. state the solution as an ordered pair. Show all work.

Answer 1

We have a system of equations:

`\begin{gathered} x+9=y \\ x=4y-6 \end{gathered}`

We can solve it by substitution, using the equality of the first equation, replacing y in the second equation:

`\begin{gathered} x=4y-6 \\ x=4(x+9)-6 \\ x=4x+4\cdot9-6 \\ x=4x+36-6 \\ x=4x+30 \\ x-4x=30 \\ -3x=30 \\ x=-(30)/(3) \\ x=-10 \end{gathered}`

With the value of x, we can calculate y as:

`y=x+9=-10+9=-1`

The solution expressed as ordered pair is (x,y) = (-10,-1).

Answer: (-10, -1)